1. Field of the Invention
The invention relates to an inertial sensor and, more specifically, to a capacitive inertial sensor that detects acceleration or angular velocity through the detection of a change in capacitance of a capacitor.
2. Description of Related Art
A conventional capacitive sensor device includes a substrate and a structure which is formed on the substrate and includes a movable mass member supported by a beam and a pair of sensing electrodes that form a differential capacitance together with the movable mass member. The sensing electrodes are fixed on the substrate, and before the measurement, namely, before the movable mass member is displaced by input acceleration, the gap (the initial gap) between the movable mass member and the sensing electrodes is fixed at a certain value. When acceleration is exerted and displaces the movable mass member, a change in differential capacitance based on the displacement is converted into a voltage output through a C-V converter (a C-V converter circuit), so that a sensor output signal is produced depending on the displacement level of the movable mass member (see, for example, Japanese Laid-Open Patent Publication No. 08-32090).
In the case of a capacitive servo-type sensor device, the potential difference between one sensing electrode and the movable mass member and the potential difference between the other sensing electrode and the movable mass member are so controlled that an electrostatic force is produced to cancel the acceleration-induced displacement of the movable mass member. In such a case, the displacement of the movable mass member is suppressed, so that an improvement in sensitivity and the desired frequency characteristic can be produced at the same time (see, for example, Japanese Laid-Open Patent Publication No. 11-326409).
The output sensitivity of a capacitive acceleration sensor (per unit of inertial force) is basically proportional to u/g0 (displacement ratio), the ratio of the amount (u) of the sensing electrode displacement produced per unit of inertial force to the initial gap (g0). In order for the conventional sensor device with the sensing electrodes fixed on the substrate to have an increased or decreased sensitivity, it is necessary to increase or decrease the displacement u of the movable mass member per unit of inertial force. This means that it is necessary to adjust the natural angular frequency ω0 (=(K/M)0.5) of oscillation, which is determined by the mass (M) of the movable mass member and the spring constant (K) of the beam supporting the movable mass member. However, this means that sensor structures should be each independently designed depending on individual desired sensitivities and that sensor devices each with a suitable natural angular frequency should be each independently manufactured; thus, this causes a problem of an increase in manufacturing cost. The resonance angular frequency is a parameter that determines the effective detection frequency (bandwidth or band) of the sensor. If the resonance angular frequency is reduced for the purpose of improving the sensitivity, the bandwidth will be narrowed. Thus, there is a tradeoff between the sensitivity of the sensor and the bandwidth.
The sensitivity can be increased simply by a reduction in the initial gap. However, the ratio of the thickness H of the structure to the feasible gap g0 (the aspect ratio H/g0) is inherently limited in terms of manufacture. Thus, the gap cannot be equal to or less than the limitation, and this means a limitation to the improvement in sensitivity.
In some cases, sticking (a pull-in phenomenon) occurs between the movable mass member and the sensing electrode (between the electrodes) by a certain difference in drive voltage for detection (a voltage difference between the movable mass member and the sensing electrode), generally depending on the configuration of the circuit for detecting the capacitance change. The pull-in threshold voltage Vth between the electrodes depends on the gap between the electrodes and the spring constant of the beam supporting the movable mass member. Thus, if the gap is reduced, the pull-in voltage should also be reduced, so that sticking can easily occur.
FIG. 34 shows a result of a simulation, in which the relationship is shown between the pull-in threshold voltage Vth and the gap g0 between the electrodes. In this example, the pull-in threshold voltage Vth is obtained using a gap g0 between parallel flat plate electrodes as a parameter under the conditions as shown in Table 1. In this example, the initial capacitance C0 (C1=C2) is 1.87 pF when the sensor device has a resonance frequency of about 6.9 kHz in the main axis-displacement direction (y direction) and an initial gap g0 of 5 μm. The pull-in threshold voltage Vth is calculated by the following formula:                               V          th                =                                            8              ⁢                                                          ⁢                              kg                0                3                                                    27              ⁢                                                          ⁢              ɛ              ⁢                                                          ⁢              ah                                                          (        1        )            
FIG. 34 indicates that: for example, an initial gap g0 of 5 μm produces a Vth of about 4.95 V; g0 of 1 μm produces a reduced Vth of about 0.44 V; g0 of 0.1 μm (100 nm) produces a further reduced Vth of 0.014 V.
TABLE 1Typical sensor structureDescriptionValueUnitThickness of capacitance-forming sensing50μmelectrodes: (h)Length of capacitance-forming electrodes:0.02108m(a)Gap between electrodes: (g0) (parameter)5μmMass of movable electrode: (M)3.27E−09kgSpring constant: (k)6.159458N/mDielectric constant, ε: (ε)8.85E−12(F/m)Young's modulus: (E)1.48E+11Pa (N/m2)
It is apparent from the result of this example that it is necessary to make the drive voltage difference very low particularly in order to prevent sticking when the gap g0 is set small, so that the electrical detection sensitivity can significantly be low.
On the other hand, it is relatively easy to increase or decrease the sensitivity by electrical amplification when a certain resistance value is selected so as to increase or decrease the amplification gain of an OP (operational) amplifier. However, the noise increases or decreases in a similar manner; thus, basically, the SN ratio (the ratio of sensitivity to noise) cannot be improved. When the effective detection frequency is kept at a given design value, and the sensitivity is increased; therefore, it is basically impossible to increase the SN ratio in proportion to the rate of rise in the sensitivity.
Sensors capable of measuring very small acceleration of the order of mG or μG have a problem that since they have high sensitivity, a shock at the time when they are attached to the measuring object can cause damage to them or sticking of the electrodes to each other, so that they can have a functional disorder.
When the movable mass member is displaced by an inertial force, the gap on one sensing electrode side can become smaller than the other because the sensing electrodes are fixed. If the gap after the displacement is significantly smaller than the initial gap (the displacement rate is high), nonlinearity of the sensor output can be high.
In a case where the input acceleration varies from moment to moment, it is necessary that maximum acceleration should be estimated and that an acceleration sensor having a range including the maximum acceleration should be used. This situation can cause a problem that measurement accuracy at a smaller acceleration than the maximum has to be lowered. In addition, if acceleration is input beyond the estimated acceleration range, the electrodes can collide with each other; thus, the sensor can have a functional disorder (such as electrode breakage).
In a servo-type acceleration sensor, the resonance angular frequency of the structure is so low that the sensitivity can be high, while an increased electrical spring constant and thus an increased electrostatic force are provided so as to suppress a reduction in bandwidth and an increase in electrode displacement of the movable mass member, which would otherwise be associated with low frequency. Concerning the servo-type sensor, therefore, a wide bandwidth or an improved linearity of the sensor output requires a high electrical spring constant, which requires a large potential difference between the electrodes. Since the potential difference between the electrodes depends on the power source for the servo-type circuit, however, the improvement in sensitivity, bandwidth or linearity of the sensor output can be limited by the upper limit of the power source for the servo-type circuit. On the other hand, a small gap between the electrodes can provide a high electrical spring constant. However, the gap can only be set small within the limitations of the production.
In the inertial sensor, the sensing electrode or the movable electrode is generally formed on (bonded to) a substrate having at least one electrical insulation, and thus has different coefficients of material linear thermal expansion or a distortion produced at the time of bonding. If the temperature of the sensor device changes, the distance between the movable electrode and the sensing electrode can also change, and the amount of the change can fluctuate, so that the capacitance between the electrodes can have a temperature dependency. This situation can cause a problem that the zero point output (the offset output) or the sensitivity of the sensor can fluctuate.
In a capacitance-detecting type inertial sensor, specifically in a capacitance-detecting oscillation-type gyro, the displacement of the movable mass member, caused by Coriolis force, which is generated at rotating mass according to the principle, is detected through a change in the capacitance formed between the fixed electrode and the movable mass member (movable electrode). In such a system, it is also relatively difficult to improve the rate of displacement or the sensitivity for the same reason as mentioned above about the acceleration sensor.